ON THE FLEXURAL VIBRATION OF RECTANGULAR-PLATES APPROACHED BY USING SIMPLE POLYNOMIALS IN THE RAYLEIGH-RITZ METHOD

Sets of simple polynomials are proposed for use as admissible functions in the Rayleigh-Ritz method, for the study of the flexural vibration of rectangular plates. The plates may be subject to a number of different complicating factors, including the presence of in-plane forces, concentrated masses, point and line spring supports and special orthotropy of the plate material. The sets of polynomials are shown to be equivalent to the orthogonally generated polynomials used very successfully in earlier studies but are more easily generated and the subsequent evaluation of the integrals in the resulting eigenvalue problem are more simply performed. Numerical results are presented for several problems, illustrating the applicability of the method and its accuracy. © 1990.